Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: why the sigma of symmetrical svd for a real symmetric matrix is negative? Date: Thu, 27 Dec 2012 04:39:09 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 9 Message-ID: <kbgjdd$bao$1@newscl01ah.mathworks.com> References: <kbgbi5$g5n$1@newscl01ah.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: www-05-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: newscl01ah.mathworks.com 1356583149 11608 172.30.248.37 (27 Dec 2012 04:39:09 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Thu, 27 Dec 2012 04:39:09 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:785455 "Rick" wrote in message <kbgbi5$g5n$1@newscl01ah.mathworks.com>... > as we know, for a real symmetric matrix A, A, there exists a singular value decomposition as A=USU', and S should be a rectangular diagonal matrix with nonnegative real numbers on the diagonal. But when I use the command schur(), > it seems that S appears negative real numbers on the diagonal as the following. Is there any problem? - - - - - - - - - - Unless your A matrix is positive definite there is no reason its singular value and schur decompositions should be the same, and the A you have defined is certainly not positive definite. In fact all its eigenvalues are negative. Check the Wikipedia site: http://en.wikipedia.org/wiki/Schur_decomposition Roger Stafford